The a1(1420) in a Unitary Coupled-Channel Three-Body Approach
Abstract
An enhancement in the three-pion energy at around √s≈ 1.42 GeV with a1 quantum numbers was observed at the COMPASS experiment. This was later attributed to the triangle singularity mechanism involving an on-shell K*(892), K and K̅ intermediate states. The alignment of the decay K with the spectator K̅ produces an f0(980), resulting in a kinematic enhancement, which is classically explained by the Landau equations. However, this one-loop process forms only part of a non-diagonal transition in a much larger coupled-channel framework. This study demonstrates the feasibility of embedding one-loop triangle-singularity calculations into a unitary three-body amplitude allowing one to consistently incorporate final-state interactions and their potentially substantial effect. For this, up to P-wave isobars and all sub-channel isospins are combined in a nine-channel production amplitude that is fitted to COMPASS lineshapes at different momentum transfers. The fitted amplitude reproduces the narrow enhancement in the (πf0)P channel near √s≈1.42 GeV. This implies that the triangle singularity mechanism sufficiently explains the observed enhancement, and an additional genuine a1(1420) pole is not required. Incidentally, the parameters of the ground state axial vector resonance (the a1(1260)) are also extracted from that data.
Versions
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BibTeX
@misc{sakthivasan2026a11420,
title = {{The $a_1(1420)$ in a Unitary Coupled-Channel Three-Body Approach}},
author = {Ajay S. Sakthivasan and Yuchuan Feng and Michael Döring and Maxim Mai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.24709},
eprint = {2606.24709},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24709},
}
RIS
TY - UNPB
TI - The a_1(1420) in a Unitary Coupled-Channel Three-Body Approach
AU - Ajay S. Sakthivasan
AU - Yuchuan Feng
AU - Michael Döring
AU - Maxim Mai
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2606.24709
UR - https://arxiv.org/abs/2606.24709
AB - An enhancement in the three-pion energy at around √s≈ 1.42 GeV with a_1 quantum numbers was observed at the COMPASS experiment. This was later attributed to the triangle singularity mechanism involving an on-shell K^*(892), K and K̅ intermediate states. The alignment of the decay K with the spectator K̅ produces an f_0(980), resulting in a kinematic enhancement, which is classically explained by the Landau equations. However, this one-loop process forms only part of a non-diagonal transition in a much larger coupled-channel framework. This study demonstrates the feasibility of embedding one-loop triangle-singularity calculations into a unitary three-body amplitude allowing one to consistently incorporate final-state interactions and their potentially substantial effect. For this, up to P-wave isobars and all sub-channel isospins are combined in a nine-channel production amplitude that is fitted to COMPASS lineshapes at different momentum transfers. The fitted amplitude reproduces the narrow enhancement in the (πf_0)_P channel near √s≈1.42 GeV. This implies that the triangle singularity mechanism sufficiently explains the observed enhancement, and an additional genuine a_1(1420) pole is not required. Incidentally, the parameters of the ground state axial vector resonance (the a_1(1260)) are also extracted from that data.
ER -